on Size, Energy and Unit, we know that the speed of light better be equal to 1, that simplify the equation of relativity.

$c = 1$

now, we impose 1 more things, the Reduced Planck constant,  $\hbar$ also set to 1. that simplify all equations with angular momentum or spin.

$\hbar = 1$

the Angular momentum:

$J^2 \left| l,m \right > = j(j+1) \hbar ^2 \left| l,m\right >$

$J_z \left|l,m \right> = m \hbar \left|l,m\right>$

now becomes :

$J^2 \left| l,m \right > = j(j+1) \left| l,m\right >$

$J_z \left|l,m \right> = m \left|l,m\right>$

when we want to calculate the real value, we can recover the $\hbar$ by considering the dimension. the reduced Planck constant has dimension

$[\hbar] = [kg][m^2][s^{-1}] = [energy][second]$

for example,

$E = \omega \hbar$